Question

Consider a spherical capacitor with radius of the inner conducting sphere a and the outer shell b. The outer shell is grounded (i.e., it is at zero potential). The charges are +Q and −Q. a A B +Q −Q b What is the magnitude of electric field at in the region between the sphere and the outer

Answer 1

The magnitude of the electric field at a point between the inner sphere and the outer shell of a spherical capacitor can be determined using Gauss's law. The formula for the electric field is E = Q / (4πε₀r²).

Step-by-step explanation:

The magnitude of the electric field at a point between the inner sphere and the outer shell of a spherical capacitor can be determined using Gauss's law. Gauss's law states that the electric flux through a closed surface is equal to the charge enclosed by the surface divided by the permittivity of the medium.

In this case, the enclosed charge is Q (since the shell is grounded and at zero potential) and the permittivity of the medium is ε₀. The electric field can be found by dividing the charge by the area of the spherical surface, which is 4πr², where r is the distance from the center of the spheres.

Therefore, the magnitude of the electric field is given by:

E = Q / (4πε₀r²)

Answer 2

Step-by-step explanation:

The application of Gauss's law is used in the derivation as shown with detailed step by step in the attached file.

The potential difference on this spherical capacitor is ΔV = Va - Vb = kQ/a - kQ/b = kQ(1/a - 1/b)